(Chorus)
All the crew was in despair
Some rushed here and some rushed there
But the Captain sat in the captain's chair
And he played his ukulele as the ship went down.

The Captain said to Seaman Jones
"You'd best put on your working clothes
While you stand and spray your hose
I can play me ukulele as the ship goes down." (Chorus)

The owners signaled to the crew
Saying, "Do the best that you can do.
We're only insured for half a crown,
We'll be out of pocket if the ship goes down." (Chorus)

The Captain's wife was on board ship
And he was very glad of it
But she could swim and she might not drown
So we tied her to the anchor as the ship went down. (Chorus)

The crow's nest fell and killed the crow
The starboard watch was two hours slow
But the Captain sang fello-de-oh-doh
And he played his ukulele as the ship went down. (Chorus)
 

It has a very Gilbert & Sullivan motif, so perhaps like "A Capital Ship" it is an early 20th Century dance hall tune.  I have found that it was composed about 1930 by Arthur LeClerc and "it was a hit for Ray Noble in the 1930s." (Thanks to Mudcat Café for the wealth of knowledge!) — Dean